Patch Antenna Design and Electromagnetic Field Simulation
Theory and Physics
What is a Patch Antenna?
Are patch antennas also inside smartphones?
The GPS antenna is exactly a patch antenna. It's formed by a thin metal patch on a dielectric substrate, offering low profile, low cost, and easy mass production. In the 5G millimeter-wave band, they are used as phased arrays.
What, that thin plate-like thing is an antenna? I had an image of a rod-like dipole antenna...
Simply put, it's a metal patch about half a wavelength in size placed on a dielectric substrate over a ground plane. Its simple structure allows it to be fabricated directly in the PCB (printed circuit board) etching process. It's used everywhere: GPS receivers, Wi-Fi access points, automotive radar, satellite communication terminals, etc.
I see! But being so thin, doesn't it have performance disadvantages?
Good observation. The biggest weakness of patch antennas is their narrow bandwidth. A typical rectangular patch has a fractional bandwidth of only about 1-5%. Also, gain is typically only around 6-9 dBi, not as high as a parabolic antenna. But the advantages of thinness, lightness, cost, and mass productivity are overwhelming. In practice, bandwidth issues are addressed with design techniques or array configurations.
Resonant Frequency and Fringing Effect
The antenna frequency is determined by the patch size, right? What's the calculation formula?
For the fundamental mode (TM₁₀) of a rectangular patch antenna, we start by calculating the effective permittivity. For patch width $W$:
Here, $\varepsilon_r$ is the substrate's relative permittivity, and $h$ is the substrate thickness. At the patch edges, the electric field fringes out beyond the substrate (fringing effect), so the electrical patch length becomes longer than the physical length $L$. This extension $\Delta L$ can be approximated by Hammerstad's formula:
Using this, we find the effective patch length and resonant frequency:
How large is $\Delta L$ actually? Is it negligible?
Not negligible at all. For example, designing a 2.45 GHz Wi-Fi antenna on an FR-4 substrate ($\varepsilon_r = 4.4$, $h = 1.6$ mm), $\Delta L$ is about 0.7 mm. With a patch length of about 29 mm, the total correction at both ends is 1.4 mm, which calculates to about a 5% shift in resonant frequency. In the GHz band, a 5% shift is critical, so fringing correction is essential.
Input Impedance and Cavity Model
How do you calculate the input impedance of a patch antenna? It needs to be matched to 50Ω, right?
There's a concept called the cavity model. We consider the space between the patch and the ground plane as a "thin resonator without walls." The top and bottom are metal walls (PEC), and the sides are open ends (PMC approximation). The two slots at the patch edges ($x = 0$ and $x = L$) function as radiation sources.
The radiation conductance $G_1$ at a patch edge is:
Including the mutual conductance $G_{12}$ between the two slots, the input impedance (resistive part) at the patch edge is:
This value is typically high, 150–300Ω. To match to a 50Ω system, the feed point is moved towards the center of the patch (inset feed). The input resistance at inset distance $y_0$ is:
Wow, it changes with $\cos^2$! So by choosing $y_0$ appropriately, we can get exactly 50Ω.
Exactly. For example, if $R_{\text{in}}(\text{edge}) = 200$Ω, then $\cos^2(\pi y_0 / L) = 50/200 = 0.25$, so $y_0 / L \approx 0.33$. In practice, we find the initial value using transmission line or cavity models, and final tuning is done with full-wave simulation. Analytical formulas alone cannot fully capture the effects of fringing, surface waves, and feed structure.
Radiation Pattern and Directivity
What shape is the radiation pattern of a patch antenna?
A rectangular patch in the fundamental mode (TM₁₀) radiates maximally in the broadside direction (perpendicular to the substrate). Due to the ground plane, there is almost no radiation to the backside. The shape differs in the E-plane (patch length direction) and H-plane (patch width direction):
E-plane ($\phi = 0$) radiation pattern:
H-plane ($\phi = 90°$) radiation pattern:
Directivity is roughly:
Does increasing the patch width increase directivity?
The H-plane beamwidth narrows, so directivity increases. However, if $W$ is made too large, higher-order modes (e.g., TM₀₂) become excited, distorting the pattern. In practice, $W$ is often kept within the range of $W \approx \lambda_0 / (2\sqrt{\varepsilon_r}) \times 1.0 \sim 1.5$. If more gain is needed, array configuration is the standard approach.
Bandwidth Estimation
I understand patch antennas have narrow bandwidth, but can we estimate how narrow beforehand?
The fractional bandwidth for VSWR $\leq 2$ can be estimated from the Q-factor of the cavity model. The total Q-factor $Q_T$ is the harmonic mean of the radiation Q $Q_r$, conductor loss Q $Q_c$, and dielectric loss Q $Q_d$:
Approximation for radiation Q:
Fractional bandwidth (VSWR $\leq 2$):
So, increasing substrate thickness lowers $Q_r$ and widens bandwidth, right?
Correct. Increasing substrate thickness $h$ lowers the Q-factor and widens bandwidth. But there's a trade-off. A thicker substrate excites surface wave modes (TM₀, TE₁, etc.), reducing radiation efficiency or increasing element coupling in arrays. As a guideline, if $h < 0.02 \lambda_0$, surface wave effects are minimal. Using a low-permittivity substrate ($\varepsilon_r \leq 2.5$) is also a standard technique for bandwidth expansion.
Why GPS Receiving Antennas are Patch Antennas
Almost all antennas in car navigation systems and smartphone GPS receivers are patch antennas. The reason is they are thin, flat, and can be printed directly on the substrate. Receiving GPS satellite signals (L1 band 1.575GHz) requires right-hand circular polarization (RHCP) characteristics. This is achieved by slightly cutting the corners of a square patch (corner truncation) or using two feed points. The design subtlety where "just a little asymmetry" creates circular polarization is hard to grasp intuitively without analysis, but watching an animation of the current distribution in simulation makes the rotating current vector immediately clear.
Physical Image of the Cavity Model
- Patch = Resonant Box Without Lid: The space between the patch and ground plane is considered a thin resonator. Top and bottom surfaces are PEC (perfect electric conductor), the four side surfaces are open (PMC magnetic wall approximation). Electromagnetic waves leak out from the sides to radiate.
- TM₁₀ Mode: The fundamental resonant mode where a half-wavelength standing wave forms along the patch length direction ($L$ direction). The two slots (open ends) at both ends radiate in phase, reinforcing each other in the broadside direction.
- Fringing = Electric Field Spillover: The electric field at the patch edges does not abruptly end at the physical edge but gradually spills out beyond the substrate. Therefore, the electrical patch length becomes longer than the physical dimension by $2\Delta L$.
- Equivalent Radiating Slots: The open ends at $x = 0$ and $x = L$ are treated as equivalent magnetic current slots of width $W$ and length $h$. The two slots, separated by $L_{\text{eff}}$, can be calculated as an array for the radiation pattern.
Patch Antenna Design Parameter List
| Parameter | Symbol | Typical Value (2.45GHz Wi-Fi) | Impact |
|---|---|---|---|
| Patch Length | $L$ | Approx. 29 mm | Determines resonant frequency |
| Patch Width | $W$ |